Math CRA

Concrete

Representational

Abstract

How will you explicitly demonstrate the use of manipulative or tools to coach concept development? What explorations and discoveries will be planned? What questions will be asked?

How can students use drawings of pictures or symbols to practice a concept independently and pave the way from the concrete level to fluency and at the abstract level?

How will you demonstrate the abstract algorithm? How will students demonstrate mastery at the abstract level?

Provide students with mat where you can write addition fact (Ex. 7+5=__)
Have students match the number of objects with the numbers in the addition fact put 7 gummy bears under the 7 and 5 under the 5.
Then have students put 7, then 5 gummy bears on the other side of the =.
Students can count up how many objects there are on each side and make sure they are the same.
Have students count up the number of gummy bears (on the right side of the =) and write the number they came up with in the blank, they found the sum of the problem.

Provide students with worksheet with an addition problem (Ex. 7+5=__)
Have students draw the number of dots there are for each number in the problem. 
Have students then put the same number of dots on the other side of the =, first 7 dots, then 5 more.
Students then can count up how many dots are on either side and make sure they are the same.
Have students count up the number of dots all together (one the right side of the =) and have them write the number in the blank, they found the sum of the problem.

Have students practice their addition facts using “Mickey’s Magical Math World” iPad app.

Concrete

Representational

Abstract

How will you explicitly demonstrate the use of manipulative or tools to coach concept development? What explorations and discoveries will be planned? What questions will be asked?

How can students use drawings of pictures or symbols to practice a concept independently and pave the way from the concrete level to fluency and at the abstract level?

How will you demonstrate the abstract algorithm? How will students demonstrate mastery at the abstract level?

Provide students with a mat with the KIND problem written on it (Ex. 10-4=___)
Have the students take out the first number of gummy bears (10) and place them on the mat.
Have the student then remove the second number of gummy bears (4) and put them back in the cup.
Students can then count the remaining gummy bears and write it in the blank, they found the difference of the problem.

Students will have a worksheet with the subtraction problem on it. (Ex. 10-4=___)
Have the students draw the number of dots to match the first number in the problem (draw 10 dots).
Then have the students cross out as many dots as in the second problem (cross out 4 dots).
The number of dots left un-crossed out should be written in the blank, they found the difference of the problem.

Have students practice their basic subtraction skills using “Match Champ Challenge” iPad app.

Concrete

Representational

Abstract

How will you explicitly demonstrate the use of manipulative or tools to coach concept development? What explorations and discoveries will be planned? What questions will be asked?

How can students use drawings of pictures or symbols to practice a concept independently and pave the way from the concrete level to fluency and at the abstract level?

How will you demonstrate the abstract algorithm? How will students demonstrate mastery at the abstract level?

Provide students with a mat with the multiplication problem written on it (Ex. 5x3=___)
Have the students read the problem, “Count by 5, 3 times.”
Have students create groups of objects. They should count out 5 paperclips into 3 groups. 
Have the students count how many paperclips there are all together and write it in the blank, they have found the product of the problem.

Students will have a worksheet with the multiplication problem on it. (Ex. 5x3=___)
Have the students read the problem, “Count by 5, 3 times.”
Have students draw 5 dots in 3 groups.
Then have the students count how many dots there are all together and write it in the blank, they found the product of the problem.

Have students practice their basic multiplication skills using “Times Tables Quiz!” iPad app.

Concrete

Representational

Abstract

How will you explicitly demonstrate the use of manipulative or tools to coach concept development? What explorations and discoveries will be planned? What questions will be asked?

How can students use drawings of pictures or symbols to practice a concept independently and pave the way from the concrete level to fluency and at the abstract level?

How will you demonstrate the abstract algorithm? How will students demonstrate mastery at the abstract level?

Provide students with a mat with the division problem written on it (Ex. 12/4=___)
Give each student 12 Starbursts. Have the student read the problem, “4 goes into 12 how many times?”
Have the students count out 4 Starbursts into groups until they run out of Starbursts or cannot make a full group of 4.
Then have the students count how many groups they created, and verify that they each have the same number of Starbursts.
Have them write the number groups on the blank, they found the product of the problem.

Students will have a worksheet with the division problem on it. (Ex. 12/4=___)
Have the students read the problem, “4 goes into 12 how many times?”
Have students draw an array of dots and group 4 together as many times as they can.
Then have students make sure each group has the same number of dots.
Have students count the number of groups and write it in the blank, they have found the product of the question.

Have students practice their basic division skills using “Multiplication and Division” iPad app.

Concrete

Representational

Abstract

How will you explicitly demonstrate the use of manipulative or tools to coach concept development? What explorations and discoveries will be planned? What questions will be asked?

How can students use drawings of pictures or symbols to practice a concept independently and pave the way from the concrete level to fluency and at the abstract level?

How will you demonstrate the abstract algorithm? How will students demonstrate mastery at the abstract level?

Provide students with a mat with the addition problem written on it (Ex.12+9 =___)
Have the students take out a matching number of Base-10 bricks as in each part of the equation, 12 and 9. They should create 12 with 1 10-stick and 2 1-blocks
Have the students count up the number of blacks all together, regrouping to a 10-stick if they count more than 10 1-blocks.
The number they count all together is the number that they fill in on the line, the found the sum of the problem.

Students will have a worksheet with the addition problem on it. (Ex. 12+9=___)
Have students draw sticks for 10s and dots for 1s for each part of the problem.
Then have students count up the total number of dots and lines, make sure they regroup to a line if they count more than 10 dots.
The total number they have at the end is what they write on the line, they found the sum of the problem. 

Have students practice their addition skills using “Math-tastic Addition” iPad app.

Concrete

Representational

Abstract

How will you explicitly demonstrate the use of manipulative or tools to coach concept development? What explorations and discoveries will be planned? What questions will be asked?

How can students use drawings of pictures or symbols to practice a concept independently and pave the way from the concrete level to fluency and at the abstract level?

How will you demonstrate the abstract algorithm? How will students demonstrate mastery at the abstract level?

Provide students with a mat with the subtraction problem written on it (Ex. 23-7=___)
Have students gather 23 base-10 blocks. This should be done using 2 10-sticks and 7 1-blocks.
Have the students take away the number of blocks in the one’s column (try to take 7 away from 3), when they realize they don’t have enough blocks, have them regroup 1 10-stick into 10 1-blocks and start over. They should be able to take 7 1-blocks away now.
Have the students count up the remaining blocks left and write it on the line, they found the difference of the problem.

Students will have a worksheet with the subtraction problem on it. (Ex. 23-7=___)
Have students draw out the equation making 2 10-lines and 3 1-dots for 23, and 7 1-dots for 7.
Have students try to cross out the number in one’s column (cross out 7 from the three), when they realize they don’t have enough dots have them regroup 1 10-line into 10 1-dots and begin again.
After crossing out the 7 1-dots, have them count up the remaining dots and write it in the blank, they found the difference of the problem.

Have students practice their subtraction skills using “Math-tastic Subtraction” iPad app.

Concrete

Representational

Abstract

How will you explicitly demonstrate the use of manipulative or tools to coach concept development? What explorations and discoveries will be planned? What questions will be asked?

How can students use drawings of pictures or symbols to practice a concept independently and pave the way from the concrete level to fluency and at the abstract level?

How will you demonstrate the abstract algorithm? How will students demonstrate mastery at the abstract level?

Provide students with a mat with the multiplication problem written on it (Ex.12 x 5 =___)
Have students read the problem, “Count by 12, 5 times.”
Then have students create groups of 12 using rulers and count how many inches make up the 5 groups.
Have students write the number they find in the blank, they found the product to the question.

Students will have a worksheet with the multiplication problem on it. (Ex.12 x 5 =___)
Have students read the problem, “Count by 12, 5 times.”
Have students create groups of 12 (1 10-line and 2 1-dots), 5 times and count the total.
Then have students write the number they find in the blank, they found the product of the question.

Have students practice their multiplication skills using “Factor Samurai – Multiplication and Division Mastery” iPad app.

Concrete

Representational

Abstract

How will you explicitly demonstrate the use of manipulative or tools to coach concept development? What explorations and discoveries will be planned? What questions will be asked?

How can students use drawings of pictures or symbols to practice a concept independently and pave the way from the concrete level to fluency and at the abstract level?

How will you demonstrate the abstract algorithm? How will students demonstrate mastery at the abstract level?

Provide students with a mat with the division problem written on it (Ex. 28/4=___)
Have students read the problem, “4 goes into 28 how many times?”
Give students 28 erasers and have them make groups of 4 until they run out of erasers or cannot make a group of 4.
When they run out of erasers, have them double check that each group has an equal number in them.
Then have students count the number of groups they made and write it in the blank, they found the product of the question.

Students will have a worksheet with the division problem on it. (Ex. 28/4 =___)
Have students read the problem, “4 goes into 28 how many times?”
Have students draw 28 dots and group them into groups of 4 until they run out of dots or they cannot make a group of 4.
Then have students check to make sure all groups have the same number of dots in them.
If they do, have students count the groups of dots and write it in the blank, they found the product of the question.

Have students practice their division skills using “Long Division Touch” iPad app.

Concrete

Representational

Abstract

How will you explicitly demonstrate the use of manipulative or tools to coach concept development? What explorations and discoveries will be planned? What questions will be asked?

How can students use drawings of pictures or symbols to practice a concept independently and pave the way from the concrete level to fluency and at the abstract level?

How will you demonstrate the abstract algorithm? How will students demonstrate mastery at the abstract level?

1. Have students partner up. Give each student a handful of Starbursts. Show question to students and have them write it on their paper.
Ex) If {Student A} has __ candies and {Student B} has __ candies. How many candies do they have all together? Have them replace Student A/B with their names and replace the blanks with how many candies they each have.
2. “What is the question?” Have students underlined what the question is asking them to do.
Ex) Have students underline “How many candies do they have all together”
3. “What do I need to do with the numbers?” Have students look at what they underlined to find if they need to add/subtract/multiply/divide.
Ex) Have students read “all together” and recognize that it’s addition. Write an + between the two groups.
4. “What are the numbers?” Have students circle the numbers in the problem.
Ex) Group {Student A’s} candy and {Student B’s} candy and have them circle around the candy and around the number representing how many candies are in each group.
5. “What is the answer?” What are they left with after following all the steps?

1. Provide a word problem on a piece of paper.
Ex) “If Adam has 9 apples and gives 7 apples to Barb, how many apples does that leave Adam?”
2. “What is the question?” Have students underlined what the question is asking them to do.
Ex) Underline “How many apples does Adam have left”
3. “What do I need to do with the numbers?” Have students look at what they underlined to find if they need to add/subtract/multiply/divide.
Ex) Have students recognize what are subtracting and have them write a “-“
3. “What are the numbers?” Have students circle the numbers in the problem.
Ex) Have students the 9 apples Adam starts with and cross off the 7 he gives to Barb.
4. “What is the answer?” What are they left with after following all the steps?
Ex) Students will see that there are 2 apples left that Adam did not give to Barb.

Have students practice their problem solving skills using “Math Word Problems” iPad app.

Concrete

Representational

Abstract

How will you explicitly demonstrate the use of manipulative or tools to coach concept development? What explorations and discoveries will be planned? What questions will be asked?

How can students use drawings of pictures or symbols to practice a concept independently and pave the way from the concrete level to fluency and at the abstract level?

How will you demonstrate the abstract algorithm? How will students demonstrate mastery at the abstract level?

Provide students with a mat with the fractions problem written on it (Ex. 8 / ¼=___)
Have students read the problem “¼ goes into 8 how many times?”
Give students 8 cups of rice. Have them scoop out ¼ cup until they run out of rice.
Then have students count how many ¼ cups they got from their 8 cups and have them write this number in the blank, they found the product of the problem.

Students will have a worksheet with the fractions problem on it. (Ex. 8 / ¼=___)
Have students read the problem “¼ goes into 8 how many times?”
Have students draw 8 bars and divide them into 4 pieces each.
Have students count how many quarters they made and write this in the blank, they found the product of the problem.

Have students practice their fraction skills using “Chicken Coop Fraction Games” iPad app.

Concrete

Representational

Abstract

How will you explicitly demonstrate the use of manipulative or tools to coach concept development? What explorations and discoveries will be planned? What questions will be asked?

How can students use drawings of pictures or symbols to practice a concept independently and pave the way from the concrete level to fluency and at the abstract level?

How will you demonstrate the abstract algorithm? How will students demonstrate mastery at the abstract level?

Provide students with a mat with the decimals problem written on it (Ex. .34 x 4=___)
Take out cool-colored (blue/green/purple) Base-10 blocks. Explain to students that these blocks hold different values than the warm colored Base-10 blocks (red/orange/yellow).
1 100-Square = 1, 1 10-stick = 0.1 or a tenth, and 1 1-block = 0.01 or one hundredth.
Have them read the problem, “Count by 34 hundredths, 4 times.”
They should collect 3 10-sticks and 4 1-blocks into four groups and count them all together and write it in the blank, they found the product of the problem.

Students will have a worksheet with the decimals problem on it. (Ex. =___)
Introduce that for decimals, 1 square = 1, 1 line = a tenth, and 1 dot = 0.01 or a hundredth.
Have the students read the problem, “Count by 34 hundredths 4 times.”
They should then draw the makings of 34 hundredths in 4 groups (3 lines and 4 dots) and count up the total. They then should write this number in the blank, they found the product of the problem.

Have students practice their decimal skills using “4th Grade Splash Math Worksheets” iPad app.

Concrete

Representational

Abstract

How will you explicitly demonstrate the use of manipulative or tools to coach concept development? What explorations and discoveries will be planned? What questions will be asked?

How can students use drawings of pictures or symbols to practice a concept independently and pave the way from the concrete level to fluency and at the abstract level?

How will you demonstrate the abstract algorithm? How will students demonstrate mastery at the abstract level?

Provide students with a mat with the ratios problem written on it (Jim sold 4 green marbles and 8 orange marbles on Monday. What fraction of the marbles Jim sold on Monday were green?)
Give students 4 green marbles and 8 orange marbles.
Have students find the total number of marbles in the problem (add the 4 to the 8) and write that as their denominator.
Then have students find the number of green marbles sold and write that as the numerator (4 green marbles).
Have students simply the fraction if necessary (4/12 --> 1/3) and write it in the blank, they found the ratio of green marbles to all marbles sold on Monday.

Students will have a worksheet with the ratios problem on it. (The lunchroom sold 4 green apples and 8 oranges on Monday. What fraction of the fruit sold on Monday were green apples?)
Have students draw 4 green apples and 8 oranges (4 green dots and 8 orange dots).
Then have students find the total number of fruit sold (add the 4 to the 8) and write that as the denominator.
Have students then find the number of green apples sold on Monday and write that as their numerator (4 green apples).
Have the students simplify the fraction if necessary (4/12 --> 1/3) and write it in the blank, they found the ratio of green apples to all fruit sold on Monday.

Have students practice their percent and ratios skills using “Thinking Block Ratios” iPad app.